1907-8.] On the Theory of the Leaking Microbarograph. 439 
Under these assumptions, the pressure, p, of the inside air is determined 
solely by its density (i.e. by the total mass of the air inside). 
Let U5 denote the pressure of the air outside, measured, like p, in 
centimetres of mercury; 2 a the internal, and 2 b the external, diameters 
of CC; 2c the diameter of AA; u and v the heights above the bottom 
of A A of the levels of the mercury outside and inside CC ; and w the 
height of any fixed point in CC', say a point in the bottom inside. 
All the lengths are supposed to be measured in centimetres. 
L L 
2 
c 
C 
IP 
A 
- 
1 A 
K 
V 
Fig. 2 
Then, if we express the condition that the pressures above and below 
the mercury surface inside CC are equal, we get the equation 
CT -p = v-u (1). 
The condition that the whole volume of the mercury remains constant is 
(c 2 - b 2 )u + a 2 v + (b 2 - a 2 )w = const. .... (2). 
The condition for the equilibrium of the floating cup gives 
b 2 u - a 2 v - {b 2 -a 2 )w = const. .... (3). 
From (2) and (3) we see that 
u = const. . . . . . (4) ; 
a 2 v + (b 2 - a 2 )w = const. . . . . (5). 
The external level of the mercury is therefore unaltered by variations 
of pressure. 
Suppose we start from the condition to which the instrument would 
